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5x^2+10x-9=3x-3
We move all terms to the left:
5x^2+10x-9-(3x-3)=0
We get rid of parentheses
5x^2+10x-3x+3-9=0
We add all the numbers together, and all the variables
5x^2+7x-6=0
a = 5; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·5·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*5}=\frac{-20}{10} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*5}=\frac{6}{10} =3/5 $
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